The h Bar

Bernardo Meurer

00:01

@SirCumference thats what you get for using proprietary malware

bolbteppa

The absolute worst is using Word with a Macros to print latex equations in it, e.g. in png form as in libreoffice, eventually, eventually, it will randomly delete all the equations and wreck everything...

Bernardo Meurer

USe libreoffife

Word is a POS software

All rich text editors are

bolbteppa

latex is the best thing ever, it's like writing a .txt file and ending up with a book printout and just a few basic rules to learn then google the rest

dmckee

00:14

@bolbteppa To get past the margin lady you need to learn more than "a few rules". We're talking black $\LaTeX$, here. Goats sacrificed to Knuth and Lamport with a silver knife on a moonless night, sorta thing.

bolbteppa

I just don't poke the margin bear/lady, even when I need to, and everything is fine

Cows

Just did laundry. Yay fresh clothes

Ok so I have to code a bit later today, then I will be waiting to get ready for my final interviews coming up. After this, I will be free to go hardcore on mathematics.

Captain Bohemian

00:59

I feel insurmountably cold.

CR Drost

01:23

So I want to build a learning resource online based on sorta how I do Stack Exchange answers, which is that there's several paragraphs of review comprising a "lesson" followed by a two-sentence answer to the question that makes sense if you have read the preceding lesson.

e.g. physics.stackexchange.com/questions/355825/… there are about 3 paragraphs of lesson and then finally I answer the question and then since it's asking about a definition and I do not like definitions I spend some extra time trying to connect this definition to real things that one would want to think about in practice.

dmckee

@CRDrost I've been building a set of very-focused, short, didactic papers for my students.

Two pages on why Schrödinger's Equation makes sense. Three pages on How to use the Euler-Legrange equation. Three more on how to use undetermined multipliers. A few pages on basic probability. Two pages on what an interval is in special relativity. And so on.

I've got about 80 pages of these things all told, now.

And they are popular enough that students not in my classes come and ask for copies.

CR Drost

that's really awesome and exactly what I want to link together.

dmckee

So I think this is a very good idea.

CR Drost

somewhere in the back of my head I am also thinking about "oh these microlessons could be a little longer", say the size of a Chinese take-out menu or so. (That is, legal paper, folded in thirds or fourths, printed on both sides with a font that allows for ~40 lines per page, minus one of these thirds devoted to a title, "this is what this lesson is about and what other microlessons it depends on."

what I wanted to ask is kind of abstract but, if there were a "food pyramid" for learning, what would your categories be on there?

dmckee

Most of mine have been upper division topics, but I think there are a lot of important topics from the intro class that would fit on a menu-folded flyer.

CR Drost

01:33

Like I would definitely have a base of the pyramid that was "examples" and at the "use sparingly" section on the top I'd have "definitions/new concepts", maybe one per flyer.

But other categories I'm not sure of, like I'm not sure if I'd do "practical application" or "theory" or w/e

dmckee

I haven't been thinking in those terms, so I'm not sure. My approach has been more on the lines of "What things did I miss the first time 'round?" and "What skills that I thought I had taught and they are going to need did my students forget immediately after taking the midterm?"

CR Drost

Those are actually really good things for me to keep in mind too

dmckee

I like to open with a introductions that "sets the notation" but also tells them exactly what they need as foundational material.

I think you are right that for a menu-lesson you don't want more than a couple of definitions. And only a few steps of mathematical derivation, if any.

CR Drost

Yeah that's actually a good point, especially if I'm thinking of this like a Wiki, trying to corral a bunch of mathematicians into using one notation is something of a loser's game. At the same time I do think LaTeX could be better if the design side were more decoupled from the semantic side so that you could be doing the derivations in something closer to Mathematica and just popping out the main result. For derivations, that's really also where hypertext shines, "link to derivation"

So we definitely need opening sections to set notation and declare dependencies on other micro-lessons or just text saying "read this chapter of that textbook, or this chapter of that textbook" or links out...

idk I am basically saying "this is in a really preliminary stage but it's been on my mind so long I think I will get angry at myself if I don't just do it to see what it becomes" and I am only one little mind so anyone else's ideas and advice would increase my abilities by an order of magnitude. :)

Even what you've already said, for you they are maybe throw-away comments but I am writing them down because there's now a whole bunch of new ideas I need to think about

dmckee

01:52

For my notes I run two-three examples from nearly trivial up to here-you-can-see-the-machinery at work and then provide a larger set of exercises that build from nearly-trivial up to more difficult than the hardest example.

Choosing a set of exercises that teach without my providing worked examples is hard, and I'm only completely satisfied on a couple of my papers so far.

CR Drost

Ooh, yes. Exercises are absolutely mandatory. Also I am a huge fan of exercises that say "provide an example of ..." or "provide a counter-example to..." that force a student to think in a college-level way and not a high-school-level way.

dmckee

Nice.

CR Drost

What are your thoughts about whether they should be interspersed through a document or collected at the end?

dmckee

I have some along the lines of "Show that [case] violates our assumption that ...", or "Compare the difficulty or working [case] with [old method] and [new method]".

@CRDrost I put mine at the end, but use directives like "Now would be a good time to work exercise 2" in the text or a footnote.

Only that burns up sapce, and if you are trying to hit a very small number of column inches it might be a problem.

peterh

03:35

@JMac Btw, all the chat communication is public on the SE. CMs, or maybe mods can make invisible rooms, but so is it.

@JMac I am not sure, if mods can see deleted posts in the chatrooms associated with other sites. Probably mods aren't chat mods on chat instances not on their sites (for example, MathSE mods probably aren't mods on chat.stackoverflow.com, but they are mods on the chat.stackexchange.com).

@JMac If my this hyphotese is okay, then a chat ban issued by a PSE mod is not active on the chat.stackoverflow.com and on the chat.meta.stackexchange.com .

SkyWalker

05:25

Any suggestions ?

@JohnRennie ???

peterh

05:57

@SkyWalker Don't worry, you've made some not very well received questions, and you've got a temporary ban for that.

@SkyWalker Try to undelete your deleted questions, at least the ones you can, and try to fix them. If you can somehow reach some upvotes, the ban will be uplifted. With time, it will be also uplifted.

@SkyWalker There are multiple "defensive walls" in the system, you probably hit only the first category. The worst is half year long, this is likely not what you want. The exact details are kept secret by the SE, because they keep everything secret what is really important, however you are free to dig in everything what is not.

@SkyWalker The PSE is not so bad for question posters as the SO, but it nears it. It is an useful strategy to ask people on the meta or on the chat, "how could I improve this question", and then doing everything what they say, if you agree it or not.

@SkyWalker But deleting your questions is a bad idea. The calculator checks 3 things: 1) question is downvoted 2) question is closed 3) question is deleted. A downvoted+closed+deleted question counts 3 times to worsen your stat. | Asking people with this "how to improve question X" is useful, because you will likely get so many tips & ideas that applying them, nothing will save your questions from a reopen :) (except the unsalvageable ones)

@SkyWalker The funny thing is, if I would be an SE starter now, I could get to 2k in a month on practically any site where I am now active... but I don't really need this knowledge any more, with my rep I am probably exempt from such bans and beginner annoyings (and, most of my questions, to my largest surprise, were quite well treated on the site)

peterh

06:19

If I get a mod message, the first what I check: does it contain a number? If it doesn't, I am already happy.

loocsieulb

07:03

@BalarkaSen ^

Slereah

>rainbow transformations

Balarka Sen

@loocsieulb absolute madlad

Sir Cumference

07:40

Should I take intro to topology or analysis first?

Anonymous

@SirCumference Complex analysis helped me get started. But the initial parts of topology is mostly some set theory stuff and the definitions of complete, closed, open, compact, etc. After that it branches out into the algebraic and geometric portions.

Sir Cumference

@Blue Hmm...welp, my current objective is to finish Real Analysis, Complex Analysis, Algebra, Intro to Topology and Intro to Differential Geometry. I just don't know a good order.

Anonymous

@SirCumference What I did was do the basics of real analysis (just undergrad level) and complex analysis from some easy textbooks. Now I'm reading the set theory and topology basics from Nash Sen and Munkres. (Nash Sen needs a considerable understanding of complex analysis)

Anonymous

I intend to learn analysis more properly this year from shakarchi stein and rudin

Sir Cumference

Erm, I don't suppose there's a Khan Academy or something similar? Those kinds of intuitive videos got me through Linear Algebra and Multivariable Calc.

Anonymous

07:47

@SirCumference Unfortunately for topology I didn't find any good video lecture series. There are some class recorded versions though.

Anonymous

(But mind you, I'm going at a very very slow pace through the books...so I might not be the best person to advise)

Sir Cumference

@Blue Wait, what year are you?

Anonymous

It's really best to sit with pen and paper and go through Nash Sen or Munkres line by line I think. That's what suits me more compared to the class recorded videos which miss out a lot of things. After those I was advised to go through Hatcher and Guillemin and Pollack (those are more advanced texts).

Anonymous

@SirCumference First year engineering

Anonymous

@SirCumference Actually @BalarkaSen is THE person to contact for topology advice

Sir Cumference

07:54

@Blue I'm always amazed by how much math the people here know...I'm 19 and I've only now gotten to the point where I'm ready for these subjects

People like you and Balarka put me in perspective

Anonymous

We don't know as much astronomy as you :)

Anonymous

Math is not a race

4

loocsieulb

08:19

stop flattering each other

it doesn’t matter how much you know just learn what you need and use it to do what you want.

Slereah

08:55

Riddle me this, topologers

if I glue two manifolds such that the metric is the same on both boundaries

Are the two boundaries isometric

Or can I glue, say, two spheres of different radius

Balarka Sen

@SirCumference intro to topology might be boring

i want to say go for analysis :)

Anonymous

Intro to topology and into to functional analysis has more or less the same topics :P One can hit two birds with one stone

Balarka Sen

intro to analysis usually doesn't mean intro to functional analysis

but true

Anonymous

Next week we have an ODE test where we can freely differentiate operators like variables, apply binomial theorem on them. This is crazy! XD (Those auxiliary equation and particular integral stuff)

Balarka Sen

Truly what physicists would do

Anonymous

09:08

lol

Slereah

if you want to annoy the professor just ask him how he defines the derivative of unbounded operators

2

Anonymous

@Slereah I did! She told me to shut up and learn operator theory :P

Slereah

(it means she doesn't know :p)

"This is the typical situation in General Relativity where the glueing of two spacetimes by means of identification of points on the boundaries is considered in order to study their possible posterior matching."

Posterior matching

I've got a match for you

My butt and your face

"Under the above assumptions, there exists a unique $C^1$ atlas on $V^4$ which induces the given $C^3$ structures on $V^+$ and $V^−$ and such that $g$ admits a continuous extension to the whole $V^4$ (and which is maximal with respect to these properties) if and only if $\Sigma^+$ and $\Sigma^−$ are isometrical with respect to their first fundamental forms inherited from $V^+$ and $V^−$; that is to say, if and only if their respective first fundamental forms $g^+$ and $g^−$ agree."

I guess it is true indeed

Cows

09:25

I'm afraid of this week lol. I guess some of the tech company rejectios will start rolling in. Hehehe

Anonymous

@Cows What type of job are you applying for?

Slereah

I guess now I have to prove what kind of surfaces and gluing give rise to properly isometric wormholes

John Rennie

@Slereah why would you want someone's face glued to your butt?

Actually, forget it - I don't want to know :-)

Slereah

It is an old American insult, @JohnRennie

It implies that both items are aesthetically similar

Anonymous

Can't be generalized to all such items

Anonymous

09:30

But wait, they aren't even homeomorphic XD

Slereah

I'm pretty glad I found that paper

It's hard to find a decent math explanation of the Israel junction condition

[@DawoodibnKareem this is not related to the Israel-Palestine conflict]

Balarka Sen

@JohnRennie The Human Centipede is an interesting horror movie

Anonymous

@BalarkaSen Eeeeeeeeeewwwwwww

Balarka Sen

(No, not really, it's disgusting, please don't watch it)

Anonymous

I did watch it once out of curiosity. Never really seen anything more puke-worthy.

Balarka Sen

09:42

well there's The Human Centipede 2

and a 3 :P

I kinda like the joke by Tom Six though. The three movies are arranged exactly like a centipede

Anonymous

@BalarkaSen Heh

Balarka Sen

(The beginning of 2 starts with a man watching 1, the beginning of 3 starts with a man watching 2)

Slereah

Symbolism, @BalarkaSen

Anonymous

That's sort of true :P

John Rennie

@BalarkaSen strangely, I've never felt the urge to watch that film :-)

Slereah

09:44

Did you watch the gross horror movie of your generation, @JohnRennie

Cannibal Holocaust

Or Pink Flamingo, depending on the kind of gross

John Rennie

@Slereah I think so. Is that the one where a crow pecks the eye out of a rotting head?

Slereah

Not that I remember

Balarka Sen

There are definitely grosser movies than The Human Centipede though

or the series thereof

David Z

@SkyWalker Read this, it explains that message fairly well:

209

Q: What can I do when getting "We are no longer accepting questions/answers from this account"?

Do not repost the question you were about to ask until you have READ EVERYTHING WE ARE ABOUT TO TELL YOU. While trying to ask a question, one could get: We are no longer accepting questions from this account. See the Help Center to learn more. Likewise, for answers: We are no longe...

Slereah

Cannibal Holocaust is the one about a film crew trying to make a fake documentary on some Amazon tribe by forcing them to commit atrocities

and then the obvious thing happens

Anonymous

09:47

If you want to see something more realistic and gruesome then watch Unit 731

Slereah

Classic 70's Italian horror movie

Anonymous

(Although they didn't depict all the realities)

Balarka Sen

I prefer over the top campy gruesomeness

Slereah

Then try Peter Jackson :p

back when he was making horror movie

Anonymous

@BalarkaSen The dark web is the place for you. :P

Balarka Sen

09:49

Bad Blood is a fun movie

anything by Henenlotter is

or whatever the fuck his name is

Dawood ibn Kareem

@Slereah I am listed in the credits of a well-known Peter Jackson movie.

Slereah

Or watch this CHILLING TALE OF TERROR

FRANKENSTEIN (1910 Edison Production) HD

►

TRIGGER WARNING : SPOOKY SKELETONS

Balarka Sen

Aw shit the background music is my jam

danse macabre

Slereah

There's also a 1910 version of the wizard of Oz and it's the worst thing

absolutely impossible to understand

Anonymous

I shouldn't have read this again: ranker.com/list/…

Slereah

10:01

"Like a scene out of The Human Centipede, the stomach would be removed and the esophagus would be attached directly to the lower intestines."

Man that's not from the human centipede

My dad had that due to stomach cancer

that's not a terribly shocking operation

although a bit on someone who doesn't need it, I suppose

Anonymous

"strapped down to operating tables and then dissected while still living without any anesthetic"

Slereah

also a bit unethical, yes

Anonymous

@Slereah That's sad to hear. Is he good now?

Slereah

Well in the sense that he's dead, I suppose

he too is a spooky skeleton now

Anonymous

:(

Slereah

10:04

I don't even know why you'd operate on someone without anesthetic

even beyond the moral issue it sounds very difficult

CooperCape

boo

Anonymous

They used to observe the subject while operating. If they did give them anesthetic, then some of the observations couldn't be recorded

Slereah

"Subject seems to be experiencing some discomfort"

Anonymous

More like how much pain you can experience till your body gives way, and you stop make any more noises (without yet dying)

Anonymous

Or so I expect

Slereah

10:07

pretty spooky and all, but not that novel compared to a lot of old timey medical experiments

Experimenting on unwilling live people was fairly common until not that long ago

Anonymous

That is true, but you know...you feel scared when you realize these were modern scientists and doctors! They were meant to cure actual Japanese soldiers and citizens.

Anonymous

They weren't illiterate barabarians

Slereah

sure, but there were also scientists in the US doing the same thing at the same time

To study syphillis and radiation poisoning

Anonymous

Indeed. I'm not denying that

Anonymous

Because other people are doing the same immoral things doesn't make that moral

Anonymous

10:11

But then again, it represents the price we had to pay to reach current level of medical advancement

Slereah

Injecting terminal patients with plutonium to see what happened

Anonymous

Something to keep in mind...

Slereah

Hm, apparently the proper junction conditions are $[g_{\mu\nu}] = 0$ and $[\partial_\sigma g_{\mu\nu}] = 0$

That would explain some things

Or... maybe not

that seems to be an additional condition

Slereah

10:44

Hm, I think the gluing function is supposed to be the isometry between the two hypersurfaces

user55789

11:38

Question about the functional determinant thingy with the path integrals. I have an action
\begin{equation}
S_E = \int_0^\beta d\tau \left(\frac12 \dot x^2 + \frac{\omega^2}{2} x^2 + \bar{\psi} \dot{\psi} + \omega \bar{\psi} \psi\right)
\end{equation}

I have done some cool stuff where I'm using the functional determinant method to evaluate the partition function. I'm getting crap but I'm not sure why, the partition function for the above reads
\begin{equation}
\mathcal Z = \frac{\det\left( \partial_t + \omega\right)}{\sqrt{\det\left(-\partial_t^2 + \omega^2\right)}}
\end{equation}

I'd like to evaluate the partition function in the orthogonal basis, i.e.
\begin{equation}
x(t) = \frac1{\sqrt{\beta}} \sum_n x_n e^{2\pi i n t/\beta}
\end{equation}
and
\begin{equation}
\psi(t) = \frac1{\sqrt{\beta}} \sum_n \psi_n e^{2\pi i (n+1/2) t/\beta}
\end{equation}

The above expression leads to a complex value up top, since the exponent is complex, i.e. I'll get
\begin{equation}
\bar{\psi}(t)\partial_t \psi(t) = \sum_n \left(\frac{\left(2n+1\right)\pi i}{\beta}\right) \bar{\psi}_n\psi_n
\end{equation}

I'm not entirely sure how to deal with the issue of a complex partition function so I'm guessing something went wrong... (?)

Curio

13:58

Is there anyone?

Slereah

No.

Curio

@Slereah do you know something about formulas of structure?

Sir Cumference

@BalarkaSen Huh, really? I'd thought taking it would get me ready for some early GR...

Slereah

intro topology is gonna be all point set topology I guess

So pretty far removed from GR

Sir Cumference

Huh...

OK, well should I take real or complex analysis first?

Slereah

14:26

0

Q: Discontinuity of metric derivatives in the Israel junction formalism

It is often said that given the metrics $g^+$, $g^-$ on two sides of a hypersurface $\Sigma$, then, with a level-set function $\phi$ such that $\Sigma = \phi^{-1}(0)$, we can describe the metric on the whole manifold by \begin{equation} g = \theta(\phi) g^+ + (1 - \theta(\phi)) g^- \end{equation...

general-relativity

plz halp

Hm, maybe I need to define the first fundamental form for every value of $\varepsilon$ along the normal bundle

Balarka Sen

14:40

@SirCumference Point-set topology, though essential to learning topology, is incredibly droll

Take complex analysis first

It's a rich subject. You'll also secretly learn some nontrivial topological notions in complex analysis

Sir Cumference

I see. Then real analysis after?

Balarka Sen

Mhm

Sir Cumference

Ok. Thanks :)

Captain Bohemian

14:52

it's like noncommutative geometry is also closely related to topology.

Slereah

Ugh

Don't remind me of non-commutatitve geometry

Talk about a headache

Captain Bohemian

it's used to propose emergent gravity.

I have not read the paper in detail, but as I browsed it, it looks interesting.

Slereah

yeah there's something about how QM can be defined as the anti-commutative version of classical variables so you can apply it to spacetime itself or something

By twisting the Lie bracket into being anticommutative or something

Captain Bohemian

why must it be anti-commutative? I consider being noncommutative is sufficient.

Slereah

oh yeah just non-commutative

I tried reading up on it but it's fairly dry

Captain Bohemian

15:03

the article regarding employing noncommutative geometry to develop emergent gravity I found is arxiv.org/abs/0809.4728.

Slereah

I tried reading this one : alainconnes.org/docs/book94bigpdf.pdf

it's not very fun

it's not the bike rides and balloons kind of non-commutative geometry

Emilio Pisanty

@JohnRennie dupehammers sure are satisfying

Captain Bohemian

15:27

@Slereah is this book written for mathematicians? I have never read such a book or paper completely. I usually read literature written for physicists.

Slereah

it's certainly not for physicists

Captain Bohemian

I may try to read this kind of article--the article for mathematicians--to see if I can understand it.

John Rennie

15:49

@EmilioPisanty Oh no, Emilio has become power crazed :-)

dmckee

16:03

@JohnRennie Well, then, he can come to our weekly mad-cackling and dry-washing-of-hands practice session.

John Rennie

:-)

All the best scientists are mad scientists

Emilio Pisanty

@dmckee finally!

I've been angling for an invite to those sessions for 5+ years

Also @dmckee it might be good for a mod to pop into that deleted thread (physics.stackexchange.com/questions/385925/…) and tell OP that there's no need to delete and it's not a great idea

dmckee

@EmilioPisanty Good idea. Done. Thanks.

Emilio Pisanty

@dmckee excellent =)

Shing

when the universe is expanding, the photon will be red-shifted. Does this mean energy is not conserved for the photon?

John Rennie

16:11

@Shing Yes

Shing

@JohnRennie thanks

oh man, that is crazy.

where does the energy go?

John Rennie

Energy isn't conserved in an expanding spacetime

There are lot of questions about this already on the site

Emilio Pisanty

... many of which have great answers by John himself

Shing

16:32

I see, thanks.

Physics Meta

17:09

0

Q: Rethinking the "too broad" criterion

I was sad this morning to see Gil Kalai's great question about the role of rigor closed for being too broad. I was even sadder this afternoon when Prof. Kalai's narrower follow-up question, was also closed for being too broad. The question also got some downvotes and, in my mind, unnecessarily co...

discussion

3

Emilio Pisanty

17:23

@PhysicsMeta @JohnRennie "I'd guess most of do to some extent"

John Rennie

@EmilioPisanty don't you find these sorts of discussions interesting? When not doing real work of course :-)

Emilio Pisanty

@JohnRennie I find picking people's typos apart exhilarating

well, no, not really, but still

John Rennie

Is there a typo there?

Admittedly there are a few other typos I need to go back and correct ...

Emilio Pisanty

@JohnRennie presumably a missing "us"

Anonymous

@JohnRennie "most of do" and "in fat" :)

Anonymous

17:26

I like your answer

John Rennie

oops yes :-)

The funny thing is that even reading your post here I failed to spot the missing us

Emilio Pisanty

@JohnRennie happens

Anonymous

(I think I'm on the same page as knzhou on this matter. But this has been discussed so many times that any further discussion would be pointless.)

Jannik Pitt

Quick question: If I have a rod and add a point mass somewhere, is the new moment of inertia the moment of intertia of the rod + the moment of inertia of the point mass? In other words is moment of inertia additive?

John Rennie

@JannikPitt Yes

The moment of inertia of any composite system is the sum of the moments of inertia of its parts.

Jannik Pitt

17:37

@JohnRennie I thought so but couldn't prove it. How would you derive that?

John Rennie

Consider how we calculate moments of inertia of objects like rods, disks, etc.

We split them up into mass elements, $dm$, and integrate $r^2dm$

In other words we just sum up $r^2 dm$ for all the infinitesimal mass elements that make up the object.

Jannik Pitt

Okay thank you

That was my reasoning too but I wanted to prove it mathematically and got an integral of some weird discontinuos function haha

Slereah

one chapter in Synge is called "The ballistic suicide problem"

"The usual problem of ballistics is to aim a projectile so that it hits someone else. Here we consider the ballistic suicide problem : the projectile is to hit the projector himself! How perverse such a problem may be sociologically, it is a neat problem in relativity, because there are only two observations and both are made by the same observer."

that's the second suicide reference I found in a GR problem

Gonenc Mogol

18:37

@Davi

@DavidZ do you know why my last spam flag was rejected? (link to the answer:physics.stackexchange.com/questions/122921/…). If I recall correctly the answer was something like "alekfj;ldsajfa;lsdkjf"

dmckee

@GonencMogol The spam flag is suppose to be reserved for attempts to sell or promote stuff. Other people who flagged that question chose "not an answer" for the most part.

Gonenc Mogol

@dmckee oh I see.. It was a "spam" in the general sense of the word but ok :)) thanks

Slereah

19:08

Why does O'neill talk about the second fundamental form but not the first

Lichnerowicz's book seem to be filled with weird GR stuff

I should look into it sometime

Slereah

19:33

It contains what seems to be Kaluza-Klein theory, except he calls it Jordan-Thiry theory

ACuriousMind

@dmckee Flagging a question as "not an answer" seems like a rather pointless action ;)

Slereah

@ACuriousMind hell of a surprise though

what's a good book for submanifolds?

ACuriousMind

Well, I would have to grant that the flag is correct, at least...

Slereah

O'neill and Lee don't seem to have a whole lot of focus on them

ACuriousMind

I think that depends on what sort of "submanifold" you're interested in and why

Not that I could recommend any, but I don't expect there to exist literature about generic submanifolds

Slereah

19:39

Lorentzian, I suppose, if need be to specialize

David Z

@GonencMogol Yeah, what @dmckee said

Phase

I'm confusing myself over really foundation things and I was wondering if I could ask some really basic questions

Basically I'm confused about why matrix multiplication is what it is, if you have defined the structure of a matrix, what's the reason for the product of two matrices being what it is? can that be justified by looking at the composite transformations on a space? And is matrix multiplication of a 1 by n and n by 1 vector really the inner product? It seems that'd give a 1x1 matrix rather than just a scalar, if there's even any significant difference

HsMjstyMstdn

Is there such a thing as reflection that's not scattering ?

ACuriousMind

@Phase Sure. Consider two square matrices $A$ and $B$ and some vector $v$. Then look at $B(Av)$ - which is "apply the transformation $A$ to $v$ and then transformation $B$ to the result" and observe that with the standard definition of matrix multiplication, that is the same as $(BA)v$, i.e. "apply the transformation corresponding to the matrix multiplication of $B$ and $A$ to $v$".

Phase

19:54

that seems more like justification that the composite transformation is the product of both matrices

ACuriousMind

As for the inner product, people are being a little bit sloppy when they say that the "inner product" is just the row times the column vector as matrices. In general, a square matrix $Q$ defines something like an inner product (it's only a true inner product when $Q$ is positive-definite) between vectors $v,w$ by $w^T Q v$ and the standard Euclidean inner product corresponds to $Q$ being the identity matrix.

Cows

@Blue well, I was applying for software engineering jobs, for verizon it had something to do with creating tools to analyze network traffic. They want to build new internal tools for that. They said no to me . .. but that's alright they aren't very bright people anyways lolz

ACuriousMind

@Phase Was that not what you were asking for with "can that be justified by looking at the composite transformations on a space?"

Phase

@ACuriousMind i'm asking how to use that to derive the actual process for multiplying the matrices, or justification that it is the way it is

ACuriousMind

@Phase And that is what I told you. To be more explicit, we are looking for the matrix $C$ such that $Cv = B(Av)$ for all $v$. Using $n$ basis vectors as $v$ in the equation, you get a linear system of $n^2$ equations which you can uniquely solve to get $C=BA$.

Phase

19:58

@ACuriousMind so I take the multiplication of an (n x m)(m x 1) a priori?

Anonymous

62

A: Why, historically, do we multiply matrices as we do?

Matrix multiplication is a symbolic way of substituting one linear change of variables into another one. If $x' = ax + by$ and $y' = cx+dy$, and $x'' = a'x' + b'y'$ and $y'' = c'x' + d'y'$ then we can plug the first pair of formulas into the second to express $x''$ and $y''$ in terms of $x$ and...

Cows

but yeh they said no too

ACuriousMind

@Phase I do not understand what you mean, can you be more explicit?

Phase

@ACuriousMind is it fine to start with the knowledge of how to multiply (n x m) and (m x 1) arrays to find how to multiply matrices?

Cows

@Blue I'm confident I will get something soon though

ACuriousMind

20:01

@Phase Ehhh, well, we have to know how to apply matrices to a vector to evaluate $B(Av)$, but that simply comes from the definition of how the matrix corresponding to a certain linear transformation is obtained in the first place

@Cows Please don't call people dicks.

Cows

@ACuriousMind oh where are me manners, sorry I forgot about the rules

ACuriousMind

Sarcasm was not the right choice there.

Phase

@ACuriousMind this is probably a dumb / vague question but if you have a type of object, is there a way of mathematically finding whether there exists a natural way to combine multiple of them to obtain another of the same type? I get it usually comes from definition but idk,

@ACuriousMind I dont think hes being sarcastic

might be wrong though

ACuriousMind

@Phase It's not a dumb question, but it's too vague to have a generic answer ;)

Phase

I think the more concerning thing though is the way you undermined the guy who was giving the interview, it was in a really weird way. Chill out @Cows

@ACuriousMind Dx

ACuriousMind

20:05

But, for instance when said objects are maps (such as linear transformations from a space to itself), the natural notion of "combining" them is just composing them.

Phase

@ACuriousMind I've actually finally started the Lin alg module in the first year, but it's really bad

the syllabus seems really basic, and my estimation of my uni is going down with each class Dx

Sir Cumference

@JohnRennie It is, but you'll obviously only deal with those kinds of scenarios in GR.

ACuriousMind

@Phase Ah well, the quality of lectures does appear to be a lottery :P

Phase

@ACuriousMind more than that there's just some really concerning things. There was a question about skew symmetric matrices and not only did no one but me or another person in the class get it, apparently it was the first year anyone did at all. Makes me think that they're probably not good at teaching

but I have no idea how to teach so I can't see what's wrong : (

Slereah

@SirCumference Well any scenario where the system isn't time-invariant

Anonymous

20:13

@Phase Do you find your classmates complaining about the quality of the lectures? If no, I guess, most of them were having trouble because they didn't have previous experience will linear algebra unlike you

Sir Cumference

@Slereah Right.

Phase

@Blue people complain about some other lecturers but I think people like this lecturer too much to complain. He doesn't really seem to have much structure, he's definitely smart and knows it but he jumps from one thing and back in tangents really often.

Anonymous

"people like this lecturer too much to complain"...that's completely possible :P

Anonymous

@Phase Which textbook do you guys use?

Phase

They haven't given out or recommended any

I mean, we're like 6 or 7 lectures in and the first 3 or 4 were spent learning how to do matrix multiplication : /

ACuriousMind

20:20

I'm not sure my (very good!) linear algebra lecturer remembered how to multiply actual matrices. When asked to do an example, he chose to multiply two matrices...over the field with characteristic two.

Phase

does that mean that (a + b)(a + b) = a^2 + b^2?

if so, I saw a meme about that

ACuriousMind

That's called freshman's dream, and yes it holds in the field with characteristic two.

Anonymous

When a meme gets so popular that is gets its own Wiki page :D

Cows

@Phase I should have shown more decorum

At any rate, still happy though :P

Oh and most importantly, I am still master of my own time

Physics Meta

20:40

0

Q: T̶h̶i̶s̶ ̶q̶u̶e̶s̶t̶i̶o̶n̶ ̶s̶e̶e̶m̶s̶ ̶l̶i̶k̶e̶ ̶a̶ ̶l̶i̶s̶t̶ ̶q̶u̶e̶s̶t̶i̶o̶n̶

This has been bothering me for a while, and I'd like to speak up about it. I see, with a much higher frequency than I would like, comments that look, with rather little variation, like This question seems like a list question. and which say nothing else at all. I would like to argue that th...

discussion close-reasons policy

0celo7

20:50

@ACuriousMind @JohnRennie my computer keeps getting random crashes when asleep for no apparent reason

I've triple checked for malware and there's nothing

what should I do?

clean Windows install?

ACuriousMind

What sort of "crashes"? Bluescreens?

0celo7

@ACuriousMind obviously the screen is black because the computer is asleep.

ACuriousMind

In any case, there should be crash logs somewhere. Find them and look for the cause of the crash

Although, maybe not when it's truly asleep

0celo7

@ACuriousMind like today I came back and all the lights were on, but it didn't respond

Cows

Going to do some accounting for a bit, then return to some client code

Emilio Pisanty

20:59

btw @0celo7 I asked an Irish person about that Ó Murchadha thing

the ch is like the soft German ch

the '-dha' is silent

0celo7

@EmilioPisanty my advisor knows the guy

Emilio Pisanty

huh

0celo7

it's O-murd-cha

@ACuriousMind the crash log has no info

it just says "Windows was not properly shut down" when I rebooted

Cows

@Phase you know, sometimes I say a lot of mean sounding things, but they should not be taken too seriously. I was kinda speaking in shall we say jest. I am sure I probably did not meet some (or many) requirements. Also I am obviously joking about the verizon people being not too bright

Just thought I would clarify this

loocsieulb

21:40

@Blue how is it a meme though?

(it was called that before memes became a thing)

Emilio Pisanty

22:03

Hey @DrNoise

I mean @DanielSank

I reckon you'll enjoy the Brownian-noise section here arstechnica.com/science/2018/02/…

Phase

22:31

@loocsieulb you're getting memed

DanielSank

@EmilioPisanty neat

@BernardoMeurer sent me this

pages.cs.wisc.edu/~kovar/hall.html

2

Emilio Pisanty

23:12

@DanielSank that's.... remarkable

vzn

lol! sounds like onion article. thats maybe ~1 decade old looking at old google results. it made it on reddit 2012. reddit.com/r/Physics/comments/11o633/… author decided to switch fields... although think a CS version could easily be written also? pages.cs.wisc.edu/~kovar/bio.html

> Having discovered that real-life physics tends to be more about fiddling with algebra than designing warp drive engines, I switched fields and entered graduate school in computer science at the Unversity of Wisconsin, Madison. I soon identified computer graphics as a field suitably tuned to my interests, and have worked in this area for the past four years. It turns out to still involve a fair amount of fiddling with algebra.

Anonymous

@DanielSank That article somewhat does represent the reality I think. Except for the very popular ones, I expect several experimental results to be erroneous. Not too many of those experiments are re-run and re-verified.

vzn

> I grew up in central Illinois and have only recently begun recovering. My undergraduate work was at Stanford, where I majored in physics. Physics is a fine major provided that you recognize that a BS in physics will not qualify you for any work requiring an extensive physics background. I recommend treating physics as a form of liberal education, more akin to english than to electrical engineering, and resigning yourself to grad school and, most likely, years as a postdoc.

Anonymous

And I've literally seen some working experimental physicists trying to forcefully do curve-fitting on data points...

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